If the area and perimeter of this rectangle are numerically equal, what is the value of $x$? Express your answer as a decimal to the nearest tenth. [asy] size(200); import olympiad; draw((0,0)--(10,0)--(10,2.5)--(0,2.5)--cycle); label("$10$",(5,0),S); label("$x$",(10,1.25),E); [/asy]
Solution: The area is $10x$ and the perimeter is $2(10+x)$. So, we solve $10x = 20 + 2x$. Subtracting $2x$ from both sides yields $8x = 20$, and dividing by $8$ gives $x = \frac{5}{2} = \boxed{2.5}$.